The sum of first three terms of an AP is 30 and the sum of last three terms is 36 - Maths - Arithmetic Progressions

Question

The sum of first three terms of an AP is 30 and the sum of last
three terms is 36 If the first term is 9 Find the number of terms
in the AP

Rishabh Mittal · Accepted Answer

Dear Student ,
Please find below the solution to the asked query :

We know ,sn=n2 2a+n-1dHere s3=30 , a=9 , n=3 
30=32 29+3-1d603=18+2d20=18+2d2=2dd=1 
Let the number of terms in A
P be n 
So,Sum of last three terms=Sum of n terms - sum of n-3 termsn229+n-11-n-3229+n-3-11=36n 18+n-1-n-3 18+n-4=72n n+17 -n-3 n+14=72n2+17n-n2-14n+3n+42=726n+42=726n=30n=5   ANS
There are 5 terms in A P 
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The sum of first three terms of an AP is 30 and the sum of last three terms is 36. If the first term is 9. Find the number of terms in the AP.